CHARLESTON, S.C. – Back on the job for his first full day, Isiah Thomas confirmed yesterday that Allan Houston has an open invitation to training camp.

However, the coach/president admitted Houston’s chances of making the Knicks roster will be challenging. The Post reported last week the Knicks were Houston’s top choice as he attempts a comeback from chronic knee problems.

Houston, who last played in 2005, is awaiting his wife giving birth to their third child.

“We’re waiting on a decision from him,” Thomas said.

Asked Houston’s chances of cracking the roster, Thomas said, “We’ll have to see. It’ll be competitive. He and I talked about that. He’s always welcome.”

Houston, 36, would become the 18th player competing for 15 slots. He’d have to beat out both veteran guard Fred Jones and second-round rookie sensation Demetris Nichols. The Knicks could make it easier on Houston if they bought out center Jerome James, already sidelined by knee tendinitis.